Idempotent ordered semigroup
Abstract
An element e of an ordered semigroup (S,·,≤) is called an ordered idempotent if e≤ e2. We call an ordered semigroup S idempotent ordered semigroup if every element of S is an ordered idempotent. Every idempotent semigroup is a complete semilattice of rectangular idempotent semigroups and in this way we arrive to many other important classes of idempotent ordered semigroups.
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